I recall that there used to be a person named Tommy that was in GunList a few years ago who sold Ithaca 37 barrels (in the 'barrels for sale' section). Unfortunately, I lost all of my back issues of GunList when I moved and have not seen the ads from him in my most recent GunLists (1999 and 2000).
You may want to contact Gun Parts Corp or Sarco to see if they have any of the Ithaca barrels available. Both companies are online and they have email addresses to send your inquiries in. I think that there was a design change in the Ithaca 37s and they might require a serial number to differentiate between the two types they had. I'm afraid that I don't know what the change was, but I had heard about it in classified ads in Shotgun News and GunList as a post or pre time dated Ithaca 37. Good luck to you.